When you run the cell, you get a dark greyish "dust" on the anode. That is silver oxide which gets pulled into the water and dissolved. The dissolution rate isn't immediate so you need to make sure you're not running at too high a current that some of it precipitates instead of dissolves.
That black "dust" is precipitated silver oxide. I can't say I've ever seen white dust but maybe you mean darker grey which usually means you banged the anode during the run and knocked off some of the silver oxide. Its quite "fragile" on the anode and it can flake off even with gentle agitation if it gets thick enough.
Just filter the reduced Colloidal Silver through a coffee filter and rinse out the jar and follow up with a distilled water rinse if you rinsed it originally with tap water (like an ounce of distilled, cap, shape, dump out and do it a second time). Tap water is BAD for Colloidal Silver. The chlorine gets in the way and there's lots of other minerals in it.
You get used to doing things a specific way over time to alleviate problems like this (more like an annoyance with this - filtering through a coffee filter is another step).
If the color of your result after reduction looks about right compared to whats shown in various posts on this site, you're good. Just filter out the "junk".